Non-relative energies from relativistic radial integrals in atoms and ions

New formulae are proposed for deriving, from ab initio relativistic results, non-relativistic approximations for the energy radial integrals relevant to the Coulomb and spin-orbit atomic interactions. For some of the electronic Slater integrals these formulae must replace those found in the literature. In the spin-orbit integrals, all contributions from the Breit-Dirac Hamiltonian are included and discussed.